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Along the Ricci flow, we study the polyhomogeneity of complete Riemannianmetrics endowed with "a Lie structure fibred at infinity", that is, a class ofLie structures at infinity that induce in a precise way a fibre bundlestructure on a certain compactification by a manifold with corners. When thecompactification is a manifold with boundary, this class of metrics contains,in particular, the b-metrics of Melrose, the fibred boundary metrics of Melroseand Mazzeo and the edge metrics of Mazzeo. Our main result consists in showingthat the polyhomogeneity of the metrics compatible with a Lie structure fiberedat infinity is locally preserved by the Ricci-DeTurck flow. If the initialmetric is asymptotically Einstein, the polyhomogeneity of the metrics solutionsis obtained as long as the flow exists. Moreover, if the initial metric is"smooth up to the boundary", then it will be also preserved by the normalizedRicci flow and the Ricci-DeTurck flow.

Polyhomog\'eni\'et\'e des m\'etriques compatibles avec une structure de Lie \`a l'infini le long du flot de Ricci